<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-03-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001689813</issuerCik>
        <issuerName>Biohaven Pharmaceutical Holding Co Ltd.</issuerName>
        <issuerTradingSymbol>BHVN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001397906</rptOwnerCik>
            <rptOwnerName>Cha Albert</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BIOHAVEN PHARMACEUTICALS, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>234 CHURCH STREET</rptOwnerStreet2>
            <rptOwnerCity>NEW HAVEN</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06510</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2018-03-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>72727</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>27.50</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2049545</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">63,903 of these shares were purchased by Vivo Capital Fund VIII, L.P. (&quot;VCF&quot;) and 8,824 of these shares were purchased by Vivo Capital Surplus Fund VII, L.P. (&quot;VCSF&quot;).</footnote>
        <footnote id="F2">The shares are held as follows: 1,800,866 shares are held by VCF and 248,679 shares are held by VCSF. The reporting person is one of the managing members of Vivo Capital VIII, LLC which is the general partner of both VCF and VCSF, and may be deemed to share voting and dispositive power over the shares held by VCF and VCSF. The reporting person disclaims beneficial ownership over such shares except to the extent of his pecuniary interest therein, and the inclusion of these shares in this report shall not be deemed an admission of beneficial ownership of the reported shares for purposes of Section 16 or for any other purposes.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Darren DeStefano, Attorney-in-fact</signatureName>
        <signatureDate>2018-03-15</signatureDate>
    </ownerSignature>
</ownershipDocument>
